1½ cups all-purpose flour
¼ cup sugar
½ teaspoon baking powder
1 stick of cold unsalted butter, cut into 12 pieces, plus more for the baking pan
1 large egg yolks
¼ cup ice water, or as needed
1½ cups chunky apricot, cherry, peach or plum preserves
Stir the flour, sugar and baking powder together in a mixing bowl. Drop in the butter and toss to coat with the flour mixture. Using the tips of your fingers, rub the butter into the flour until the pieces of butter resemble small corn flakes. Work quickly to keep the butter as firm as possible. Beat the egg yolk and 1/4 cup ice water in a separate small bowl until blended. Drizzle over the flour-butter mixture and toss just until you have a rough dough. Don't overmix. If there are some pieces of unmoistened dough, drizzle more ice water, about 1 teaspoon at a time over the dough and toss lightly to mix. Turn out onto a work surface and knead lightly a few times, just to gather the dough into a ball. Wrap the dough tightly in plastic wrap and refrigerate at least 1 hour or up to 1 day.
Lightly butter an 8-inch square baking pan. Preheat the oven to 350 degrees F. Cut off and set aside one-third of the dough. Roll out the remaining two-thirds of the dough on a lightly floured surface to a 9 x 9-inch square. Flour the surface lightly as necessary to keep the dough from sticking. Transfer the dough to the prepared pan, cover the bottom completely and pressing the dough about 1/2 inch up the sides of the pan. Spoon the preserves in an even layer over the dough. Roll out the remaining dough to a circle about 8-inches in diameter. Cut the dough into 1/2-inch strips. Form a lattice pattern over the preserves with the strips of dough by arranging half of them diagonally over the filling, then laying the second half of the dough strips perpendicular to the first. Bake until the dough is golden brown, about 25 minutes. Remove and cool completely before cutting into 36 squares. Crostate cookies can be stored in an airtight container at room temperature for up to 5 days.